A novel r-circulant block Jacket transform with fast algorithms

Abstract

Jacket transform inspired by the well-known Hadamard transform, has been attracting more and more attentions due to its orthogonality, simpleness of its inversion and fast algorithms. It has also been applied to signal processing, image compression, mobile communication, quantum coding, and so on. In this paper, we firstly propose the r-circulant block Jacket transform (r-CBJT) to extend the Jacket transform family, and then we suggest an approach for the elegant construction of the r-circulant block Jacket matrices (r-CBJMs) with any size by using the structure of the permutation matrices. After that, the fast construction and decomposition algorithms for the r-CBJMs can be designed with the Kronecker product of corresponding identity matrices and relative lower order Jacket matrices in a successively iterative form. It has a less computation complexity compared to direct calculation approach, which is vitally important and practical to some real-time applications, such as high-speed mobile wireless communication, instant audio and video transmission, fast encoding and decoding, and so on.